So, by moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case
What is diffraction?
When waves flow through an aperture or around objects, they spread out, which is referred to as diffraction. It happens when the wavelength of the incident wave and the size of the aperture or obstruction are on the same order of magnitude. The majority of the wave is blocked at extremely small aperture diameters. Large apertures prevent severe diffraction from occurring as the wave passes past or through the obstruction.
What is wavelength?
Wavelength is the separation between the corresponding points of two successive waves. When two points or particles are referred to be "corresponding points," it means that they are both in the same phase means, points that have completed identical fractions of their periodic motion.
Hence, by moving the slit towards the laser will increase the slit and screen distance, and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case.
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which nonmetal family is the most reactive on the periodic table
) suppose the distance to the moon were twice its actual value. could we still have solar eclipses? if so, what type(s)?
Answer:
I think we still could have solar eclipse but with it blocking sun by being more small
by what factor does the gravitational force between two objects increase if one object doubles in mass and the distance between them decreases by half?(1 point)
The gravitational force between two objects increase if one object doubles in mass and the distance between them decreases by half F = 8G m1 m2 / r^2.
Because F = G*m1*m2/r2,
G * 2m1 * m2 / (r/2)2 = 8G m1 m2 / r2, which is the right answer if m1 doubles and r falls by half.
Objects with mass are drawn toward one another by the gravitational attraction, also known as the force of gravity. The gravitational force of the Earth is something we consider frequently. Your body is kept stationary on the ground by this force. However, every other mass-containing item experiences a gravitational pull from every other mass-containing object. Gravity is a fundamental interaction in physics that produces mutual attraction between all things having mass or energy (from the Latin gravitas, "weight". By far the weakest of the four fundamental interactions, gravity is 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force, and 1029 times weaker than the weak interaction. As a result, it has no discernible impact on the level of subatomic particles. But the most important relationship is gravity.
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Given the discussion above, can you argue that the propagation of error/uncertainty formula for a non-linear model is more general and can be used for a linear model?
Statisticians say that this type of regression equation is linear in the parameters. However, it is possible to model curvature with this type of model. While the function must be linear in the parameters, you can raise an independent variable by an exponent to fit a curve.
Define Linear regression?
Linear regression is easier to use, simpler to interpret, and you obtain more statistics that help you assess the model. While linear regression can model curves, it is relatively restricted in the shapes of the curves that it can fit. Sometimes it can’t fit the specific curve in your data.
Define Nonlinear regression?
Nonlinear regression can fit many more types of curves, but it can require more effort both to find the best fit and to interpret the role of the independent variables.
Thus, Statisticians say that this type of regression equation is linear in the parameters. However, it is possible to model curvature with this type of model. While the function must be linear in the parameters, you can raise an independent variable by an exponent to fit a curve.
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as a participant in a research study, jolan is required to report what he is doing and how he is feeling using a smartphone app when he receives an alert. he receives alerts at two random times each day. jolan is most likely participating in research.
As a participant in a research study, Jolan must report what he is doing and how he feels using a smartphone app when he receives an alert. He receives alerts at two random times each day. Jolan is most likely participating in participatory research.
Participant observation (PO) is a research technique in which the researcher actively participates in the daily activities of the participants. The objective is to record conduct under the widest range of possible settings.
Researchers work with community members to understand and resolve community problems, empower community members, and democratize research. The participatory research methods include group discussions of personal experience, interviews, surveys, and analysis of public documents.
The question is incomplete. The correct question is
As a participant in a research study, Jolan is required to report what he is doing and how he is feeling using a smartphone app when he receives an alert. He receives alerts at two random times each day. Jolan is most likely participating in ______ research.
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using the procedure in this experiment explain how the measured density of a substance is affected for each of the following: will the density be falsely high or falsely low? a. When weighing a volumetric flask full of water, a student does not notice that the outside of the flask is wet.
b. When weighing an empty beaker, a student does not notice that there is some water inside
For (a) effect on density when weighing volumetric flask full of water, is that it comes out to be falsely high.
For (b) effect on density when weighing an empty beaker, the density of water would be falsely low.
Now, let's see the given two cases:
(a) If when weighing the flask full of water, there are some droplets of water on the outside, we realize that these droplets would contribute to the mass being measured, but would not be factored in the volume of water (which is the volume of the flask). Hence, the mass in the expression above would be larger than expected.
The effect on the density is that it would turn out to be falsely high.
(b) In this case, we are at the stage of the procedure where we have emptied the beaker and need to ascertain its mass. The purpose for this step is to find out the mass of the water alone. We would subtract the mass of the beaker alone from the mass of the beaker with water. Now, if there is some little water inside the beaker which the student assumes to be empty, the mass of the beaker alone would turn out slightly higher than is true. Hence, the mass of the water alone would in turn come out to be slightly lower than accurate.
Now, Observing the formula for density, the mass would be smaller than accurate, and the density of water would be falsely low.
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true or false? an air-conditioning system changes the temperature of the air, but does nothing to clean the air
It is true that an air-conditioning system changes the temperature of the air, but does nothing to clean the air.
How does air conditioning system operate?An air conditioner is a system that is used to cool down a space by removing heat from the space and moving it to some outside area. The cool air can then be moved throughout a building through ventilation.
The air-conditioning system helps keep our environment to our desired temperature. Cooling is generally achieved in the air conditioning system through a refrigeration cycle, but sometimes evaporation or free cooling is employed.
Therefore, it can be said that an air conditioner only regulates ambient temperature but does not purify the air.
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discuss why you think the frictional torque that slows down the spinning cylinder should or should not affect your results here.
Friction is a self adjusting force. In plain words, it means that if there is an increase in linear velocity, then there shall be an increase in angular velocity as well.
Friction is a self adjusting force . It adjusts with appreciate to external force. Importantly, the static friction is any intermediate value less than the most static friction. In simple phrases, it approach that if there is an boom in linear pace, then there will be an increase in angular velocity as nicely.
Paintings accomplished through force is calculated as the dot manufactured from pressure and displacement of point of software of force. In case of angular motion, force is changed by way of torque and linear displacement is replaced by angular displacement.
The conventional instance of that is a spinning ice skater or a person spinning in an office chair. via pulling in her arms, the skater decreases her second of inertia, so her angular speed has to boom so that it will keep her angular momentum constant.
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15. you want to horizontally push a 6kg box across the floor. frictional force is 4n. how hard must you push it to have it accelerate at 0.8m/s2 ?
A force of 8.8 N is required to horizontally push a 6kg box across the floor with frictional force of 4N and acceleration of 0.8 [tex]m/s^{2}[/tex].
We know that [tex]F = m*a[/tex] ,where m = mass and a= acceleration.
When a frictional force acts, then
[tex]F = m*a + F_{friction}[/tex]
Given m = 6kg
a = 0.8 [tex]m/s^{2}[/tex]
[tex]F_{friction}[/tex] = 4N
Putting these values in above equation we get F = 8.8N.
i.e. A force of 8.8 N is required to horizontally push a 6kg box across the floor with frictional force of 4N and acceleration of 0.8 [tex]m/s^{2}[/tex].
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when acetylcholine binds postsynaptic nicotinic acetylcholine receptors, each receptor causes its own postsynaptic voltage change, which is called an end-plate potential. the summation of the end-plate potentials represents the membrane potential. the synaptic acetylcholine concentration influences the amplitude of end-plate potentials.
An ion pore is created in the receptor as a result of a conformational shift brought on by the binding of two acetylcholine molecules to a nicotinic AchR.
Acetylcholine binds to the nicotinic receptors localized on the motor end plate, a specific region of the post-synaptic membrane of the muscle fiber. The nicotinic receptor channels open as a result of this binding, allowing sodium ions to pass into the muscle fiber. Acetylcholine diffuses across the synaptic cleft after being released from synaptic vesicles and binds to acetylcholine receptors on the postsynaptic membrane. The acetylcholine receptor is a pentameric protein made up of five subunits. Acetylcholine binds to the nicotinic receptors concentrated on the motor end plate, a specific region of the post-synaptic membrane of the muscle fiber. The nicotinic receptor channels open as a result of this binding, allowing sodium ions to pass into the muscle fiber. The adrenal cortex contains nicotinic cells, which produce hormones. Both sympathetic and parasympathetic preganglionic neurons are all nicotinic.
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when an inductor and a resistor are connected in parallel, how many degrees out of phase are the current flow through the resistor and the current flow through the inductor?
Its current flow through resistor and the flow of current through the inductor are 90 degrees out of phase whenever an inductor and just a resistor are coupled in parallel.
What is a resistor used for?An resistor is an electrical component that regulates or limits the amount of electrical current that can flow through a connection in an electronic gadget. Resistors can be used to deliver a certain voltage to the an active element like a transistor.
What is resistor and its unit?The electricity cannot travel because a resistor, a weak electrical component, introduces resistance. Almost all circuits or electrical networks have them. Resistance is measured in ohms ().
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considering higher frequencies, what is the next frequency that will be canceled out upon reflection with this distance between rows?
283.33Hz is the next frequency that will be canceled out upon reflection with this distance between rows.
How might you define frequencies?The number of waves that pass through a fixed location in a specific amount of time is known as frequency. As a result, if a wave travels for 1/2 second, the frequency is 2 per second. 100 times per hour is the frequency if it takes 1/100 of an hour.
Given,
L = 1.5
n = 2
Vs = 340
By using following formula calculate λ:
L = (n+1/2)λ/2
1.5 = (2+1/2)λ/2
1.5 = 5λ/4
λ = 1.5×4/5
λ = 1.2
By using following formula calculate frequency:
Vs = fλ
f = 340/1.2
f = 283.33Hz.
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Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of radon-218 to decay from 99 grams to 0. 50 grams? the half-life of radon-218 is 35 milliseconds.
It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.
We know that half life of a first order reaction is given by: [tex]t_{1/2} = 0.693/k[/tex]
where k = rate of reaction
Given half life = 35 milliseconds
So from this we get k = 0.0198
Now we know that rate of first order reaction is given by: [tex]kt= 2.303 * log(R'/R)[/tex]
where t= time
R'= initial amount = 99 g
R= final amount= 0.50 g
k= rate of reaction = 0.0198
Putting values of these in above equation we get t=267 milliseconds.
i.e. It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.
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what is the maximum speed the electron could have after the collision? express your answer with the appropriate units.
The maximum speed of the electron after collision is
1,258,107 m/s
What is collision?
Any instance in which two or more bodies exert forces on one another quickly is referred to as a collision in physics.
What are the 3 types of collision?
There are three different types of collisions: elastic collisions and inelastic collisions. collision with perfect inelasticity.
I understand that the question you are looking for
The allowed energies of a simple atom are 0.0 eV, 3.5 eV and 5.0 eV . An electron traveling at a speed of 1.5×106 m/s collisionally excites the atom. Part A What is the minimum speed the electron could have after the collision?What is the maximum speed the electron could have after the collision?
The electrons can move from 0.0 eV to 5.5 eV and from 5.5 eV to 9.0 eV, respectively.
The smallest energy difference, from 5.5 to 9.0, is 4.5 ev.
Then, using the equation KE = (1/2)m*v2, we must determine the electron's speed to obtain a kinetic energy of 4.5 ev.
Where,
KE = 4.5 ev * 1 J / (6.242*1018) ev = 7.2098*10 19 J
m = 9.11 x 10 -31 kg, where m is the mass of the electron.
v = (2 * KE/m) = [2*7.2098* 10-19 kg/(9.11*10-31 kg)] = 1,258,107 m/s
In response, 1,258,107 m/s
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how much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.20 ss ? assume it is a solid cylinder.
Given:
Mass of the merry-go-round, m= 1640 kg
Radius of the merry-go-round, r = 7.50 m
Angular speed, = ω = (1/8) rev/sec
= (2π * 7.8) / 8 rad/sec
= 5.89 rad/sec
Therefore, force required,
F = m * ω² * r
= 1640 * (5.89)² * 7.5
= 427126.9 N
Thus, the net work done for the acceleration is given by :
W = F x r
= 427126.9 x 7.5
= 3,203,451.75 J
Therefore, the net work done is 3,203,451.75 J
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS : A 1640 kg merry-go-round with a radius of 7.50 m accelerates from rest to a rate of 1.00 revolution per 8.00 s. Estimate the merry-go-round as a solid cylinder and determine the net work needed for this acceleration.]
a collection of molecules holding a charge of 14 coulomb all pass through a hole in 4 seconds. what is the current (in amps) through the hole?
The current that passes through the hole is 3.5A
What is current?The rate at which electrons flow past a point in a complete electrical circuit is defined as current. At its most fundamental, current = flow. An ampere (AM-pir), also known as an amp, is the international unit for measuring current.Although current is the flow of electrons, current and electron flow in opposite directions. Electrons flow from negative to positive while current flows from positive to negative. The number of electrons passing through a conductor's cross-section in one second determines current.Here given ,
Charge = 14 coulomb
Time = 4 sec
We have to current,
I = Q/t
Where Q is the charge and t is time in seconds.
By substituting the values,
I = 14/4
I = 3.5A
Therefore the current through the hole is 3.5A.
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You perform 100 j of work on a refrigerator that extracts heat from a cold reservoir and dumps heat into a hot reservoir. The amount of heat dumped into the hot reservoir must be.
From the first law of thermodynamics, we have 100 J of heat that we would dump in the hot reservoir.
What is the first law of thermodynamics?We know that thermodynamics has to do with the area of science that studies the exchange of heat. Heat is that which could cause the temperature of an object to rise. Thus heat can also be defined as a form of energy that owes to the difference in temperature between the objects.
From the first law of thermodynamics, we have been told that energy is neither created nor destroyed but we can convert it from one form to another in the system. Here we are told that you perform 100 J of work on a refrigerator that extracts heat from a cold reservoir and dumps heat into a hot reservoir.
This implies that the same amount of heat is dumped.
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find the capacitance of a parallel plate capacitor if the area of each plate is 0.1 m2 and the distance between the plates is 0.1 inch. the dielectric is air.
The capacitance of a parallel plate capacitor is 3.612×10⁻¹⁰ohm if the area of each plate is 0.1m² and distance between plate is 0.1inch.
Capacitance is the capacity of a material item or gadget to store electric charge. It is estimated by the adjustment of charge because of a distinction in electric potential, communicated as the proportion of those amounts. Regularly perceived are two firmly related thoughts of capacitance: self capacitance and shared capacitance.
An article that can be electrically charged shows self capacitance, for which the electric potential is estimated between the item and ground. Common capacitance is estimated between two parts, and is especially significant in the tasks of the capacitor, a gadget intended for this reason as a rudimentary straight electronic part.
We know that 1inch=2.54cm
Therefore,0.1inch=2.54×0.1cm=0.245cm=0.00245m
Now, we know that capacitance=∈[tex]_o[/tex]×A /d where
∈[tex]_o[/tex] is the permittivity of free space,
A is the area of cross-section,
d is the distance between two plates.
We know that value of ∈[tex]_o[/tex]=8.85×10⁻¹² Farad/meter
Therefore, C = (8.85×10⁻¹²×0.1)/0.00245
=>C=(8.85×10⁻¹³)/0.00245
=>C=3.612×10⁻¹⁰ohm
Hence, value of capacitance is 3.612×10⁻¹⁰ohm.
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if the coefficient of kinetic friction between tires and dry pavement is 0.83, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 21.2 m/s ?
The shortest distance required to to stop the automobile by locking the brakes is 27m.
The coefficient of friction is 0.83 between tires and dry pavement.
We have to find the shortest distance in which the automobile should come to stop from 21.2m/s.
The net acceleration of the automobile is,
a = Fr/m
Fr is the frictional force,
m is the mass of the body,
a= ug
g is the gravitational acceleration.
Putting values,
a = 0.93 x 9.8
a = 8.31 m/s².
Now, using the equation of motion,
V² - U² = 2as
s is the stopping distance,
V is the final speed,
U is the initial speed,
a is the acceleration of the automobile.
Putting values,
(21.2)² = 2 x 8.13 x s
s = 27m.
So, the stopping distance of the automobile is 27m.
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Disk A, with a mass of2.0 kgand a radius of90 cm, rotates clockwise about a frictionless vertical axle at30rev/s. Disk B, also2.0 kgbut with a radius of40 cm, rotates counterclockwise about After the collision, what is magnitude of their common angular velocity (in rev/s)? that same axle, but at a greater height than disk A, at30rev/s. Disk B slides down the axle until it lands on top of disk A, after which they rotate together. Part B In which direction do disks rotate after the collision?
The negative sign indicates that the rotations are clockwise i.e. -872.206rad/s
We are given that,
Mass A = m = 2.0kg
Radius A = r = 90cm
Radius B = 40cm
Let's apply the idea of angular number conservation to the rotation of a disc. We construct a system composed of the two discs, where the forces that last the shock are internal at the beginning.
L₀ = I₀ w₀ + I₁ w₁
Thus the instate final. Right after crash
Lf = (I₀ + I1) w
angular momentum is conserved
I₀ w₀ + I₁ w₁ = (I₀ + I₁) w
w = I₀ w₀ + I₁ w₁ / Io + I1
The moment of inertia of a disk with an axis passing through its thermometric center can be calculated by ,
I₀ = ½ m² r₀²
I₁ = ½ m₁ r₁
I₀ = ½ 2.0 × 0.90²
I₀ = 0.81 kg. m
I₁ = ½ 2.0 0.4²
I₁ = 0.16 kg .m
Therefore ,let's reduce the magnitudes the SI system
w₀ = -40rev / (2πrad / 1rev) = -251.2rad/s
w₁ = 90rev (2πrad / 1rev) = 565.2 rad/s
we will assume that the counterclockwise turns are positive
w = (-0.81) (251.2) + (0.16)(565.2) / (0.81 + 0.16)
w = (- 203.47 + 90.432)/ .1296
w = - 113.038/.1296
w = - 872.206rad/s
The negative sign indicates that the rotations would be in clockwise direction.
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Once you set a ball rolling in a frictionless bowling alley, the force needed to keep it rolling is.
None of the options are appropriate in In a bowling alley with no friction, the force required to keep a ball rolling is minimal.
What does a frictionless encounter entail?What Is a Customer Experience Without Friction? Friction is any obstacle that slows down or dissatisfies a customer during their interaction with a business. The simplest definition of frictionless customer service is monitoring the customer journey and improving the customer experience.
Are smooth and frictionless synonymous?By frictionless, what do you mean? A frictionless surface is not possible since a smooth surface will have greater static friction than a rough surface because there will be more electromagnetic forces acting on both surfaces. Additionally, the author just wants to disregard friction on flat surfaces.
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in circular motion there must be a centripetal force directed the center.target 1 of 4 at the bottom of the swing trajectory we can pretend you are in uniform circular motion, so the net force points toward the center of the circle.target 2 of 4 therefore, the swing must exert a force on you than the earth does in the downward direction.target 3 of 4 so, your apparent weight is your true weight.
The concepts used to solve this problem are force, apparent weight, true weight and circular motion.
When the object is at swing and at the bottom of the swing trajectory, we can predict that the object is in uniform circular motion. To maintain the circular motion, a force acts towards the center of the path. Hence, the object has two forces acting on it. The two forces are, force due to gravity and the centripetal force. At the bottom of the arc, the object requires a maximum force to hold it in its circular path.
Apparent weight defines the heaviness of a given object. When the force of gravity and normal force does not balance each other, the apparent weight of an object will differ from the weight of an object.
When an object is in uniform circular motion, it will experience a centripetal force towards the center of circular path.
The expression for force due to gravity is,
F = mg
The second one is centripetal force along with the force due to gravity which is exerted by swing directed upwards.
F = mg + mv²/r
Therefore, the swing must exert a larger force on the object in an upward direction than to the earth in the downward direction.
At the lowest point, the resultant force is,
Fr = N-mg
The resultant force supplies the centripetal force:
N=mg + mv²/r
Here, mg is the actual weight.
An additional centrifugal force also acts with the actual weight.
Therefore, the apparent weight is greater than true weight.
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find q1 , the volume of fluid flowing into the pipe per unit of time. this quantity is also known as the volumetric flow rate. express the volumetric flow rate in terms of any of the quantities given in the problem introduction.
The q1 is the pipe diameter, v is the velocity of the fluid, and π is the constant 3.14.
What is velocity?
When an object is moving, its velocity is indeed the direction it is moving in as a measure of how quickly its position is changing as seen from a specific point of view and so as measured by a specific unit of time, such as 60 km/h in a northerly direction. Kinematics, the area of classical mechanics which studies how bodies move, uses the concept of velocity as a fundamental building block. It takes both direction and magnitude to define velocity, a physical vector quantity. Speed is a coherent derived unit that expresses the scalar absolute value (amplitude) of velocity. Its quantity is expressed in SI (metric system) units of meters per second (m/s or ms1). The terms "5 metres per second" and "5 metres per second east," for instance, denote scalar and vector, respectively.
The volumetric flow rate can be expressed in terms of the pipe diameter, the velocity of the fluid, and the cross-sectional area of the pipe.
Volumetric flow rate = (cross-sectional area)(velocity)
Volumetric flow rate = (π x (q1/2)²) x v
where q1 is the pipe diameter, v is the velocity of the fluid, and π is the constant 3.14.
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a particle p moves with simple harmonic motion. state, with reference to motion of p, what is meant by simple harmonic motion
Answer:
Simple harmonic motion is a type of periodic motion where the restoring force on the moving particle is proportional to the magnitude of the objects displacement and acts towards the particle's equilibrium position.
Explanation:
magnetic resonance imaging needs a magnetic field strength of 1.5 t. the solenoid is 1.8 m long and 75 cm in diameter. it is tightly wound with a single layer of 2.0-mm-diameter supercon- ducting wire. what size current is needed?
The current required for MRI of strength has 5.67A.
A patient is positioned inside a large magnet for the purpose of obtaining an MRI image, and they are required to maintain extreme stillness throughout the imaging procedure to prevent image blurring.
A patient may receive intravenous contrast materials (often containing the element gadolinium) before or during the MRI to hasten the rate at which protons realign with the magnetic field.
The image becomes brighter as the protons realign more quickly.
B=1.5T
l=1.8m
a=2mm=0.02m
[tex]i=\frac{2dB}{y}[/tex]
=2 x 0.02 x 1.5/1.8
=5.67A
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what total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?
The total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water is 9 L
How to calculate total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?The space occupied within an object's borders in three dimensions is referred to as its volume. It is referred to as the object's capability on occasion.
Assuming that gasoline has a density of 750 kg/m3 and steel has a density of 7800 kg/m3 as the density of gasoline is not specified.
There are 2 constraints: 1. volume of steel + volume of gasoline = volume of water and at the threshold of sinking, 2. mass of steel + mass of gasoline = mass of water
240L * 1m³ / 1000L = 0.240 m³
first: Vs + Vg = Vw = Vs + 0.240m³
second: ρs*Vs + ρg*Vg = ρw*Vw → substitute for Vw, Vg and all the densities
7800*Vs + 750*0.240 = 1000*(Vs + 0.240) (7800 - 1000)*Vs = 240 - 750*0.240 Vs = 60 / 6800 = 0.00882 m³ = 8.82 L ≈ 9 L
Therefore total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water is 9 L
The complete question is : Because gasoline is less dense than water, drums containing gasoline will float in water. suppose a 240-l steel drum is completely full of gasoline. part a what total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?
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a distant quasar shows a large redshift -- one so large, in fact, that the features we now see in the visible-light region of the spectrum would be invisible to us, were it not for the redshift. what band of the electro-magnetic spectrum were these features most likely in, before the spectrum was redshifted?
Answer:
Explanation:
a circular curve of highway is designed for traffic moving at 60 km/h. (a) if the radius of the curve is 150 m, calculate the correct angle of banking of the road. (b) if the curve were not banked, calculate the minimum coefficient of friction between tires and road that would keep traffic from skidding at this speed.
The angle of banking of the road is 11° and The minimum coefficient of friction between tires and road is 0.19
The attached free-body diagram to the query illustrates the forces operating on the car if the road is banked at an angle without utilizing friction (i.e., frictionless road).
mg = N cos θ (Eqn 1)
mg = weight of the car.
N = normal reaction of the plane on the car
And in the direction parallel to the inclined plane,
(mv²/r) = N sin θ (Eqn 2)
(mv²/r) = force keeping the car in a circular motion
Divide (Eqn 2) by (Eqn 1)
(v²/gr) = Tan θ
v = velocity of car = 60 km/h = 16.667 m/s
g = acceleration due to gravity
r = 150 m
(16.667²/(9.8×150)) = Tan θ
θ = Tan⁻¹ (0.18896)
θ = 10.7° ≈ 11°
b) In the absence of banking, the force maintaining the car in a circular motion must be balanced by the frictional force of the road.
That is,
Fr = (mv²/r)
Fr = μN = μ mg
μ mg = mv²/r
μ = (v²/gr) = (16.667²/(9.8×150)) = 0.19
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if the coefficient of kinetic friction between tires and dry pavement is 0.96, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 20.3 m/s ?
The shortest distance in which you can stop an automobile by locking the brakes is 59.3m
The frictional force acting on the car is
F(f) = -μmg
where
μ = 0.81 is the coefficient of friction
m is the mass of the car
g = 9.8 m/s^2 is the acceleration due to gravity
According to Newton's second law, the acceleration of the car is equal to the frictional force divided by the mass, so:
a = F(f)/m = -μg = -(0.81) (9.8m/s²) =
-7.9m/s²
So we can find the distance travelled by the car using the equation
v^2 - u^2 = 2ad
where v = 0 is the final velocity of the car, when it comes to a stop
u = 30.6 m/s is the initial velocity
Solving the equation for d, we find
d = v^2 - u^2/2a = 0-(30.6m/s)^2/2(-7.9m/s^2) = 59.3m
Hence, The shortest distance in which you can stop an automobile by locking the brakes is 59.3m
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A 0.260 kg potato is tied to a string with length 2.50 m, and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of support, with the string pulled taut, and is then released.A) What is the speed of the potato at the lowest point of its motion? let g be = 9.80 m/s^2
The speed of the potato at the lowest point of its motion is calculated to be 7 m/s.
The total energy of an object remains constant or changes its form from one energy to another in an isolated system as per the law of conversation of energy.
Therefore, in this case, the potential energy of the potato will be equal to its kinetic energy when the sting is pulled taut and the potato will be released.
Potential Energy = Kinetic Energy
mgh = 1/2 ( mv^2)
Here m represents the mass of the potato,g is the gravitational force on the potato, h is the height of the string, and v represents the velocity of the potato
Substituting the values to determine the speed of the potato at the lowest point of its motion as follows;
0.260 × 9.80 × 2.50 = 1/2 × (0.260 × v^2)
v^2 = 49
v = √49
v = 7 m/s
Therefore, at the lowest point, the potato's speed will be 7 meters per second.
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